Final answer:
The nerve that controls the PNS, specifically for the stimulation of smooth muscle in the GI tract, is the vagus nerve (Cranial Nerve X). It is part of the autonomic nervous system and acts via the myenteric plexus to regulate GI motility.
Step-by-step explanation:
This nerve that controls the Peripheral Nervous System (PNS), which stimulates the contraction and relaxation of the smooth muscle in the gastrointestinal (GI) tract, is the vagus nerve which corresponds to Cranial Nerve X (10). The vagus nerve is part of the autonomic nervous system and regulates the function of the enteric nervous system through its parasympathetic fibers. The intrinsic innervation of the alimentary canal is provided by the enteric nervous system, with the myenteric plexus being responsible for the motility of the GI tract, including the rhythm and force of muscular contractions.
Therefore, when the question asks which nerve controls the PNS that affects the GI tract's smooth muscle contractions, the correct answer among the choices provided, referencing Roman numerals, would be C. VI (which is the vagus nerve, also known as Cranial Nerve X).